In [1]} Mann-Rafi gave a CB generating set for \(\operatorname{FMap} (\Sigma )\)  and \(\operatorname{Map} (\Sigma )\) .
Let \(L\)  be the surface of finite-type as above. The first collection of elements in our
generating set are the elements fixing \(L\)
\(\nu _{L} = \big \lbrace g \in \operatorname{Map} (\Sigma ) \mathbin {\mid }g|_L = id \big \rbrace .\) 
